Strength of materials question

A rigid steel plate is supported by three posts of high-strength concrete each having an effective cross-sectional area A =40000 mm2 and length L = 2 m. Before the load P is applied, the middle post is shorter than the others by an amount s = 1.0 mm.

A rigid steel plate is supported by three posts of high-strength concrete each having an effective cross-sectional area A =40000 mm2 and length L = 2 m. Before the load P is applied, the middle post is shorter than the others by an amount s = 1.0 mm.

Working aswell as diagram are shown in the pdf attached. Just looking for feedback on how I completed the question as it just seemed a little to easy for an assignment question?? cheers

Yes, not that easy. The middle column doesn't take nearly as much load as the outer ones, which have taken up most of the load before the middle column sees any load at all. The load is equally shared amongst the three only after the first 1 mm of deflection in the outer ones.

To start with, I do not feel that the assumption of a "rigid" steel plate is realistic. In structural analysis, everything deforms under load, and that is the basis of inderterminate structures like this present one.

However, since no physical information is available for the steel plate, we will have to live with the assumption of the plate being rigid.

The loading of the three columns progresses in two stages, with respective load capacities of F1 and F2.

F1 represents the total force required to deform the two outer columns to a deformation of 1 mm, as you have correctly calculated.
F2 represents the additional load shared by all three columns until one or more columns bust under σallow = 18 MPa. It is obvious that F2 is equally shared by all three columns because of the "rigid" assumption, and therefore the additional stress capacity of
σ = 18 MPa - 15 MPa = 3 Mpa.

If you do the detailed calculations, you will find that F1+F2 = 1.56 Mpa.